To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size?

4.5 < c < 12
4.5 ≤ c ≤ 12
c < 4.5 or c > 12
c ≤ 4.5 or c ≥ 12

Why: If Elisa doesn't use more than 4.5 oz of clay that means that the maximum amount of clay she uses for a small vase is 4.5, and that she usually uses less than that.

The phrase "at least" indicates a "greater than or equal to" sign, ≥.

Why: If Elisa uses at least 12 oz of clay for large vases then she uses at a minimum of 12 oz and usually uses more than that.

Finding the Answer

We can eliminate the top two answer choices because,

if she uses more than 12 oz of clay--like she normally does for her big vases--it would not satisfy either inequality

if she uses less than 4.5--like she normally does for her small vases--, it wouldn't satisfy either inequality

which our final answer should account for.

Since we found the inequality signs we can also eliminate the third one as it uses "less than" and "greater than" signs.

Thus it leaves us with the bottom answer choice as our final answer.

Verification

We can plug in values into our chosen answer choice to verify that it's the correct answer.

We said that Elisa usually uses less than 4.5 oz for her small vases and more than 12 oz for her bigger ones.

Looking at these two inequalities,

if we plugged in c = 1 into c ≤ 4.5, it would be satisfied (true).

Similarly,

if we plugged in c = 15 into c ≥ 12, it would also be satisfied.

Thus this is the final answer.